THE ANALYSIS OF CIRCULAR PLATES VIA NEURO-FUZZY TECHNIQUE

Mühendislik sistemlerinin analizi genelde sayısal tekniklere dayanmaktadır. Yüzeysel taşıyıcı sistemler günümüze kadar çeşitli sayısal metotlar ile çalışılmıştır. Bu çalışmada dairesel plakların analizi, farklı bir hesaplama tekniği olarak son yıllarda kullanılmaya başlanan mantıksal programlama tekniği ile verilmiş ve geliştirilen program yardımıyla çeşitli örnekler çözülmüştür. Yapay sinir ağını eğitmek için çok farklı eğitim seti kullanılmış ve yeterli hassasiyet sağlanmıştır. Ağın eğitimi sırasında bağlantı ağırlıklarının ve kullanılan temel değişkenlerin belirlenmesinde fuzzy küme teorisinden faydalanılmıştır. Elde edilen sonuçlar, sayısal teknikler ile elde edilen sonuçlar ile karşılaştırılmış ve mantıksal programlama tekniğinin yapı mühendisliğinde kullanılabilecek alternatif bir metot olduğu vurgulanmıştır. The analysis of engineering systems are generally based on numerical technique. Surfaces portal systems had been studied with different numerical methods until now. In this study, the analysis of circular plates is given with logical programming technique which has been used in the recent years as a different programming technique and various examples are solved by means of developed program. Various training sets are used to train the artificial neural network and sufficient sensibility is maintained. Fuzzy set theory is used during the training of the network, evaluation of the connections weights and determination of the basic variables used in training of network. The obtained results are compared with the results of the numerical techniques and it has been emphasized that logical programming technique is an alternate method which can be used in structural engineering

ON THE NUMERICAL SOLUTION OF SOME BOUNDARY VALUE PROBLEMS VIA GENERALIZED DIFFERENTIAL QUADRATURE METHOD

Gerek mühendislik sistemlerinin analizinde ve gerekse uygulamalı disiplinlerde diferansiyel denklemlerin çözümü büyük bir öneme sahiptir. Çoğunlukla bir sınır değer ve/veya başlangıç değer formunda olan bu denklemlerin analitik çözümü çoğu durumda mümkün değildir. Bu amaçla yeter yaklaşıklıkta çözümler elde etmek için günümüze kadar pek çok sayısal analiz yöntemi geliştirilmiştir. Bu yöntemlerin her birinin; gerektirdikleri bilgisayar kapasiteleri, zaman ve hassasiyet açısından biri birine göre avantajları ve dezavantajları mevcuttur. Çalışmada genelleştirilmiş diferansiyel quadrature metodu kısaca tanıtılmış, mühendislikte ve temel bilimlerde sıkça karşılaşılan bazı tür sınır değer probleminin sayısal çözümü sunulmuştur. Genelleştirilmiş diferansiyel quadrature yönteminin bilinen bazı tip diferansiyel denklemlerin çözümünde kullanılacak alternatif bir metot olduğu vurgulanmıştır. The solution of differential equations has a great importance in the analysis of engineering systems and applied disciplines. It is not always possible to obtain the analytical solutions of these equations, which has a boundary value and/or initial value form as usual. For this purpose, it has been improved many numerical analysis method to obtain the adequate solutions up to now. All of these methods have a relative advantage and disadvantage with respect to each other because of the time aspect and the sensitivity. In this study, Generalized Differential Quadrature (GDQ) method was briefly introduced and presented the numerical solutions of some type boundary value problems that have been confronted in engineering and basic sciences often. It has been emphasized that generalized Differential Quadrature method is an alternate method for the solution of known type differential equations

A nonlocal sinusoidal shear deformation beam theory with application to bending, buckling, and vibration of nanobeams

This paper presents a nonlocal sinusoidal shear deformation beam theory for the bending, buckling, and vibration of nanobeams. The present model is capable of capturing both small scale effect and transverse shear deformation effects of nanobeams, and does not require shear correction factors. Based on the nonlocal differential constitutive relations of Eringen, the equations of motion as well as the boundary conditions of the beam are derived using Hamilton’s principle. Analytical solutions for the deflection, buckling load, and natural frequency are presented for a simply supported beam, and the obtained results are compared with those predicted by the nonlocal Timoshenko beam theory. The comparison firmly establishes that the present beam theory can accurately predict the bending, buckling, and vibration responses of short nanobeams where the small scale and transverse shear deformation effects are significant

Bending Response of Nanobeams Resting on Elastic Foundation

In the present study, the finite element method is developed for the static analysis of nano-beams under the Winkler foundation and the uniform load. The small scale effect along with Eringen's nonlocal elasticity theory is taken into account. The governing equations are derived based on the minimum potential energy principle. Galerkin weighted residual method is used to obtain the finite element equations. The validity and novelty of the results for bending are tested and comparative results are presented. Deflections according to different Winkler foundation parameters and small scale parameters are tabulated and plotted. As it can be seen clearly from figures and tables, for simply-supported boundary conditions, the effect of small scale parameter is very high when the Winkler foundation parameter is smaller. On the other hand, for clamped-clamped boundary conditions, the effect of small scale parameter is higher when the Winkler foundation parameter is high. Although the effect of the small scale parameter is adverse on deflection for simply-supported and clamped-clamped boundary conditions

Structure–property relation and relevance of beam theories for microtubules: a coupled molecular and continuum mechanics study

Quasi-one-dimensional microtubules (MTs) in cells enjoy high axial rigidity but large transverse flexibility due to the inter-protofilament (PF) sliding. This study aims to explore the structure–property relation for MTs and examine the relevance of the beam theories to their unique features. A molecular structural mechanics (MSM) model was used to identify the origin of the inter-PF sliding and its role in bending and vibration of MTs. The beam models were then fitted to the MSM to reveal how they cope with the distinct mechanical responses induced by the inter-PF sliding. Clear evidence showed that the inter-PF sliding is due to the soft inter-PF bonds and leads to the length-dependent bending stiffness. The Euler beam theory is found to adequately describe MT deformation when the inter-PF sliding is largely prohibited. Nevertheless, neither shear deformation nor the nonlocal effect considered in the ‘more accurate’ beam theories can fully capture the effect of the inter-PF sliding. This reflects the distinct deformation mechanisms between an MT and its equivalent continuous body

Temperature-dependent nonlinear analysis of shallow shells: A theoretical approach

The paper presents a theoretical formulation for the computation of temperature-dependent nonlinear response of shallow shells with single and double curvatures subjected to transverse mechanical loads while being exposed to through-depth non-uniform heating regimes such as those resulting from a fire. The material nonlinearity arises from taking into consideration the degradation of the material elastic behaviour at elevated temperatures under quasi-static conditions. Two types of boundary conditions are considered, both of which constrain the transverse deflections and allow the rotations about the edge axis to be free. One of the boundary conditions permits lateral translation (laterally unrestrained) and the other one does not (laterally restrained). A number of examples are solved for shallow shells under different types of loading conditions including: an exponential "short hot" fire leading to a high temperature over a relatively short duration; and an exponential "long cool" fire of lower temperature over a longer duration. The limits of the shallow shell equations are investigated through comparison studies. Results show that while current numerical approaches for analysis of laterally restrained shallow shells are often computationally intensive, the proposed approach offers an adequate level of accuracy with a rapid convergence rate for such structures.The Edinburgh Research Partnership in Engineering (ERPE)